Understanding Hyperporphyrin Spectra: TDDFT Calculations on Diprotonated Tetrakis(p-aminophenyl)porphyrin

A detailed TDDFT study (with all-electron STO-TZ2P basis sets and the COSMO solvation model) has been carried out on the effect of diprotonation on the UV–vis–NIR spectra of free-base tetraphenylporphyrin and tetrakis(p-aminophenyl)porphyrin. The diprotonated forms have been modeled as their bis-formate complexes, i.e., as so-called porphyrin diacids. The dramatic redshift of the Q-band of the TAPP diacid has been explained in terms of an elevated “a2u” HOMO and lowered LUMOs, both reflecting infusion of aminophenyl character into the otherwise classic Gouterman-type frontier MOs. The exercise has also yielded valuable information on the performance of different exchange–correlation functionals. Thus, the hybrid B3LYP functional was found to yield a substantially better description of key spectral features, especially the diprotonation-induced redshifts, than the pure OLYP functional. Use of the range-separated CAMY-B3LYP functional, on the other hand, did not result in improvements relative to B3LYP.


■ INTRODUCTION
Porphyrins are notorious for leaving stains on glassware. Most tetraphenylporphyrins are dissolved by acid, which transforms their characteristic purple color to a brilliant green. The color change corresponding to diprotonation of tetraphenylporphyrin (H 2 [TPP]) is associated with modest redshifts of both the Soret and Q bands, from 417 and 646 nm to 443 and 659 nm, respectively. 1 Much more dramatic spectral changes are observed for meso-tetrakis(p-aminophenyl)porphyrin (H 2 [TAPP]), for which protonation of the two unprotonated central nitrogens results in redshifts of the Soret and Q bands, originally at 438 and 669 nm in DMSO, to 467 and 813 nm, respectively ( Figure 1). 2 In addition to the redshift, the Q-band also dramatically gains in intensity. Martin Gouterman 3 and coworkers, using semiempirical calculations, recognized these redshifts as a form of hyperporphyrin character, 4 reflecting charge transfer from the meso-aryl groups. 5 Modern quantum chemical methods, however, have not been applied to H 2 [TAPP] and its diprotonated form. 6−8 As it happens, even unprotonated H 2 [TAPP] exhibits a number of peculiarities. Thus, unlike most para-substituted tetraphenylporphyrins, which exhibit optical spectra that are qualitatively indistinguishable from parent H 2 [TPP], H 2 [TAPP] exhibits significantly redshifted Soret and Q bands. Second, the oxidation potential of H 2 [TAPP] is substantially lower than that predicted on the basis of a Hammett correlation applicable to the great majority of para-substituted tetraphenylporphyrins. 2 Taken together, these results suggest that the HOMO of H 2 [TAPP] is unexpectedly high in energy and that the amino substituent acts differently from other para substituents. Is H 2 [TAPP] itself to be viewed as an incipient hyperporphyrin?
The above phenomena, while of interest in and of themselves, are relevant to a number of practical applications. As dyes absorbing in the near-infrared (NIR), hyperporphyrins are clearly of interest in photomedicine, for example, as photosensitizers in photodynamic therapy. 9−13 Protonated porphyrins have been used as sensors for gases such as ammonia, hydrogen sulfide, and sulfur dioxide, 14,15 while H 2 [TAPP] has also been used as a building block for dye-sensitized solar cells. 16−18 Porphyrin protonation has also been used for pH 19,20 and anion sensing 21 and even for modulating the optical properties of metal−organic frameworks (MOFs). 22 Thus, motivated, we sought to shed light on the above spectral shifts via timedependent (TD) density functional theory (DFT) 23  ■ RESULTS a. The Theoretical Model. The term "theoretical model" emphasizes the assumptions underlying our study and encompasses a number of aspects. A key aspect, obviously, concerns the exact chemical nature of the molecules studied, especially of the diprotonated forms of the porphyrins. Here we have modeled them as highly symmetric (D 2d ) bis-formate adducts. These adducts, also known as porphyrin diacids, 30,31 are experimentally well-known and have been structurally  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article characterized. These models also have the advantage of being charge-neutral, which should help stave off spurious transitions that may result in the presence of unbalanced charges (a relatively common issue in TDDFT calculations). A second, related aspect concerns solvation, which also helps deter spurious transitions in TDDFT calculations. The results quoted below all refer to the COSMO 32 solvation model and dichloromethane as solvent. Experimentally, both DMSO and dichloromethane have been used. 1,2,8 We also examined the PCM 33 model (with the Gaussian program) and found that it does not make much of a difference relative to COSMO.
Finally, the choice of the exchange−correlation functional turned out to be important. We began our study using OLYP 34,35 -D3, 36 OLYP being a generalized gradient approximation that has been extensively calibrated in our laboratory.
The calculations indeed yielded valuable insights and assignments but also evinced a number of shortcomings that we wished to improve upon. Thus, OLYP predicted excessively large redshifts for the Q bands of the porphyrin diacids ( Figure 2 and Table 2). The same calculations also predicted an intense transition (at 628 nm) between the main Soret and Q features of TAPP diacid, for which there does not appear to be an experimental counterpart (Figure 1).
The above problems were largely solved with B3LYP 37,38 and its range-separated counterpart CAMY-B3LYP. 39−41 Thus, both these functionals yielded Q-band redshifts that agreed well with experiment. Somewhat surprisingly, CAMY-B3LYP did not lead to improved results relative to B3LYP. We speculate that adjusting the amount of exchange in the B3LYP functional may well result in even better agreement between theory and   Figure 3) provides substantial insight into the observed spectral shifts and the hyperporphyrin effect and nicely sets the stage for a discussion of spectral assignments. The relevant MOs are depicted in Figure 4.
Of the four species examined, only H 2 [TPP] conforms strictly to the Gouterman four-orbital model; 42,43 i.e., the two HOMOs are energetically close and the two LUMOs are essentially degenerate and these 4 MOs are energetically well-separated from all other MOs. That said, we shall see that the main optical transitions of all four species do conform to a largely Gouterman-type four-orbital composition. Below, although we will generally describe key MOs in terms of their actual irreducible representations (irreps), on occasion we will also use the well-known D 4h irreps, within quotation marks, to facilitate allusion to the four-orbital model.
For strongly saddled TPP diacid, the "a 2u " HOMO (which transforms as b 2 under D 2d ) drops marginally in energy relative to H 2 [TPP] (Figures 3 and 4). The drop appears to be associated with a slightly greater delocalization of the MO onto the phenyl groups relative to parent H 2 [TPP]. The LUMOs undergo a sharper drop, reflecting substantial delocalization onto the phenyl groups. These orbital energy shifts result in a significant contraction of the HOMO−LUMO gap, qualitatively explaining the Q-band redshift observed (11−13 nm, depending on the solvent; Table 1) upon protonation of H 2 [TPP]. The "a 1u " HOMO (transforming as b 1 ) also drops sharply, away from the "a 2u " HOMO ( Figure 3). These changes in orbital energy are best viewed as the combined effects of protonation, the resulting strong saddling, and enhanced porphyrin-phenyl conjugation as a result of the latter; it is unclear whether the individual effects of the three factors can be rigorously dissected into separate, additive contributions.
Compared with H 2 [TPP], H 2 [TAPP] exhibits a slight rise in the LUMO energy levels and a sharper rise in the energy of the "a 2u " HOMO ( Figure 3), understandably, given the large amplitudes of the latter MO at the meso positions ( Figure 4). The result is again a contraction of the HOMO−LUMO gap, coincidentally to about the same value as for TPP diacid.
TAPP diacid exhibits LUMO energy levels slightly higher than those of TPP diacid, but the energy of the "a 2u " HOMO (transforming, again, as b 2 ) is considerably higher (Figures 3 and  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article 4), reflecting the combined effects of protonation, strong saddling, and para-amino substitution. The HOMO−LUMO gap accordingly is dramatically contracted, qualitatively consistent with the extremely redshifted Q-band of TAPP diacid. Interestingly, although the "a 1u " MO has approximately the same energy as that in TPP diacid, it corresponds to HOMO−4/HOMO−5 in TAPP diacid, depending on the functional. Between the "a 2u " and "a 1u " HOMOs, lie 2−3 aminophenyl-based MOs, disrupting the simple four-orbital model. c. Spectral Assignments. Tables 2−4 present the detailed TDDFT data, including the MO-to-MO composition of key transitions for OLYP, B3LYP, and CAMY-B3LYP. Although the three functionals tell the same broad story, the reader may readily verify that the latter two functionals yield excitation energies (wavelengths) in significantly better agreement with experiment ( Figure 1 and Table 1).
As expected, the Q and Soret transitions of H 2 [TPP] exhibit a classic Gouterman four-orbital composition (Table 1). Thus, the two near-degenerate Q features (Q x and Q y ) may be described as primarily HOMO → LUMO and HOMO → LUMO+1 transitions, while the two Soret features may be described as primarily HOMO−1 → LUMO and HOMO−1 → LUMO+1 transitions, respectively. In terms of composition, the The calculated, degenerate Q transitions of TAPP diacid may be described as essentially pure "a 2u " → LUMO (e) transitions. The strongly redshifted position of the transition appears 2-fold in origin, an elevated "a 2u " HOMO and lower-energy e LUMOs, relative to H 2 [TAPP]; both effects reflect infusion of aminophenyl character into the classic Gouterman-type frontier MO in question. The "a 1u " HOMO of TAPP diacid, in contrast, is lower in energy, relative to H 2 [TAPP], which explains a modest protonation-induced redshift for the Soret band. Interestingly, while B3LYP does a good job of reproducing the observed Soret redshift, CAMY-B3LYP predicts a small blueshift instead.
A major difference between B3LYP and CAMY-B3LYP concerns the Soret region of TAPP diacid. Thus, while B3LYP predicts two Soret-like features at 459.6 and 501.6 nm ( Figure 2 and Table 3), CAMY-B3LYP predicts a unique, dominant Soret maximum at 445.1 nm (Figure 2 and Table 4). As indicated in Table 3, the 501.1 nm peak with B3LYP is a degenerate pair of aminophenyl → LUMO (e) transitions. Such transitions also The Journal of Physical Chemistry A pubs.acs.org/JPCA Article occur with CAMY-B3LYP, but with much weaker intensities and on the higher-energy side of the major Soret peak (Table 4).

■ CONCLUSION
A first TDDFT study of tetraphenylporphyrin and tetrakis(paminophenyl)porphyrin diacids has afforded substantial insight into the origin of their hyperporphyrin spectra. 44 In short, multiple effects account for hyperporphyrin spectra. Two different effects are primarily responsible for the Q-band redshifts. For diacid formation, the major contributor to the Qband redshifts is a lowering of the LUMOs as a result of infusion of meso-aryl character. Elevation of the "a 2u " HOMO also plays a role, albeit a smaller one. In contrast, the redshifted Q-band of H 2 [TAPP] relative to H 2 [TPP] reflects destabilization of the "a 2u " HOMO via interaction with aminophenyl-based occupied MOs, while the LUMOs remain energetically relatively unperturbed.
Beyond the Q bands (i.e., for the Soret bands as well as certain pre-Soret and post-Soret bands), the transitions of the diacid forms are compositionally more complex. In these, meso-aryl → LUMO character mixes in with classic Gouterman "a 1u " → LUMO transitions. Indeed, some of these transitions may be described as primarily meso-aryl or aminophenyl-based; the intensities of these transitions appear to vary significantly with the exchange−correlation functional.
An important finding, from a methodological point of view, is that the hybrid functionals B3LYP and CAMY-B3LYP perform much better than the pure functional OLYP. Use of the rangeseparated CAMY-B3LYP functional, however, does not appear to confer any significant advantage relative to classic B3LYP. Additional functionals, as well as solvent effects, are being examined in our laboratory. Overall, the above study has led to straightforward insights into an important class of hyperporphyrin spectra, which, we believe, should significantly aid in the design of a variety of porphyrin-based functional materials such as phototherapeutics, sensors, and solar dyes.

■ COMPUTATIONAL METHODS
All calculations were carried out with the ADF 45 2018 program with all-electron ZORA-STO-TZ2P basis sets, fine meshes for numerical integration of matrix elements, and adequately tight convergence criteria for both SCF and geometry optimization cycles. Molecular geometries were optimized with OLYP 34,35 -D3 36 with appropriate symmetry constraints (as indicated in Chart 1e); these optimized geometries were then used for TDDFT calculations with the OLYP-D3, B3LYP, 37